Here me out, please.
When Dez complains and begs and makes demands to Romo in the huddle or on the sideline, Romo just rolls his eyes and walks away. He barely hears it, and when he's tired of hearing it, he basically tells Dez to "shut the **** up!" It doesn't change a thing about how Tony plays. Dez has to just deal with it and accept it. Same for Brady, Rodgers, Manning, etc. They just don't hear you or care what you think much.
However, big-time receivers with big personalities like Dez don't often mix well with lesser backup quarterbacks. Too often, those quarterbacks get intimidated and rushed into throwing to those receivers no matter the coverage or situation. It clouds the thinking of the quarterback, who's head is spinning and emotions are overflowing already. Defenses can sense it and adjust.
Weeden just needs to play the game these next few weeks. Nothing more. Throw to the open guy, take care of the ball, but otherwise, don't worry about anything and just play. There'll be no big egos to deal with. Witten won't be screaming in his ear for the ball. They'll band together as a team.
That's not to say Dez is a bad team guy, because he isn't. He's just so passionate and selfish (all great receivers are) that it gets the best of him. And it can be a challenge for players not at his level to manage.
If Weeden can get a few games under him and gain some confidence, then it could be a big boost if Dez can return before Romo. But for at least these first few games, there's a silver lining to him being out.